document.write( "Question 186956: Here is another problem i have been trying to figure out how to do.
\n" ); document.write( "John can fill the pool in 30 min, Sue can fill the pool in 45 min, and Sam can fill it in 90 min how long would it take all three of them to fill the pool together?
\n" ); document.write( "I have the answer but dont know how to get the answer. I have asked everyone
\n" ); document.write( "I can think of for help including one of my teachers and still can't figure it
\n" ); document.write( "out.
\n" ); document.write( "I have figured out how much of the pool each can fill in 15 min which is half
\n" ); document.write( "the time it takes the fastest to fill the pool and several different ways but
\n" ); document.write( "can't figure out how to do it. \n" ); document.write( "

Algebra.Com's Answer #140139 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
Edwin's solution:
\n" ); document.write( "

\r\n" );
document.write( "Make this chart\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "       Number of pools filled = Rate in pools per minute  × Time required\r\n" );
document.write( "John  |                       |                           | \r\n" );
document.write( "Sue   |                       |                           |   \r\n" );
document.write( "Sam   |                       |                           |\r\n" );
document.write( "-------------------------------------------------------------------------\r\n" );
document.write( "All 3 |                       |                           | \r\n" );
document.write( "\r\n" );
document.write( "Since the question asks:\r\n" );
document.write( "

\n" ); document.write( ">>...How long would it take all three of them to fill the pool together?...<<
\n" ); document.write( "

\r\n" );
document.write( "We let T represent the time required for all 3 to fill it, so we put \r\n" );
document.write( "x in the bottom right position in the table, for that's the time for\r\n" );
document.write( "all 3.  We also fill in 1 for the number of pools \r\n" );
document.write( "\r\n" );
document.write( "       Number of pools filled = Rate in pools per minute  × Time required\r\n" );
document.write( "John  |                       |                           | \r\n" );
document.write( "Sue   |                       |                           |   \r\n" );
document.write( "Sam   |                       |                           |\r\n" );
document.write( "-------------------------------------------------------------------------\r\n" );
document.write( "All 3 |          1            |                           |       x \r\n" );
document.write( "\r\n" );
document.write( "

\n" ); document.write( ">>...John can fill the pool in 30 min...<<
\n" ); document.write( "

\r\n" );
document.write( "So that's 1 pool, so we put in 1 for the number of pools that John\r\n" );
document.write( "fills, and we put in 30 for his time required to fill that 1 pool: \r\n" );
document.write( "\r\n" );
document.write( "       Number of pools filled = Rate in pools per minute  × Time required\r\n" );
document.write( "John  |          1            |                           |      30\r\n" );
document.write( "Sue   |                       |                           |   \r\n" );
document.write( "Sam   |                       |                           |\r\n" );
document.write( "-------------------------------------------------------------------------\r\n" );
document.write( "All 3 |          1            |                           |       x\r\n" );
document.write( "

\n" ); document.write( ">>...Sue can fill the pool in 45 min...<<
\n" ); document.write( "

\r\n" );
document.write( "So that's 1 pool, so we put in 1 for the number of pools that Sue\r\n" );
document.write( "fills, and we put in 45 for her time required to fill that 1 pool:\r\n" );
document.write( "\r\n" );
document.write( "       Number of pools filled = Rate in pools per minute  × Time required\r\n" );
document.write( "John  |          1            |                           |      30\r\n" );
document.write( "Sue   |          1            |                           |      45 \r\n" );
document.write( "Sam   |                       |                           |\r\n" );
document.write( "-------------------------------------------------------------------------\r\n" );
document.write( "All 3 |          1            |                           |       x\r\n" );
document.write( "

\n" ); document.write( ">>...Sam can fill it in 90 min...<<
\n" ); document.write( "

\r\n" );
document.write( "So that's 1 pool, so we put in 1 for the number of pools that Sam\r\n" );
document.write( "fills, and we put in 90 for his time required to fill that 1 pool: \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "       Number of pools filled = Rate in pools per minute  × Time required\r\n" );
document.write( "John  |          1            |                           |      30\r\n" );
document.write( "Sue   |          1            |                           |      45 \r\n" );
document.write( "Sam   |          1            |                           |      90\r\n" );
document.write( "-------------------------------------------------------------------------\r\n" );
document.write( "All 3 |          1            |                           |       x\r\n" );
document.write( "\r\n" );
document.write( "Next we fill in the rates by this formula:\r\n" );
document.write( "\r\n" );
document.write( "Rate =  (Number of pools filled)/(Time required)\r\n" );
document.write( "\r\n" );
document.write( "That is we put the number of pools filled over the time:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "       Number of pools filled = Rate in pools per minute  × Time required\r\n" );
document.write( "John  |          1            |           1/30            |      30\r\n" );
document.write( "Sue   |          1            |           1/45            |      45 \r\n" );
document.write( "Sam   |          1            |           1/90            |      90\r\n" );
document.write( "-------------------------------------------------------------------------\r\n" );
document.write( "All 3 |          1            |            1/x            |       x \r\n" );
document.write( "\r\n" );
document.write( "Now the rate for all three must equal the sum of their rates.\r\n" );
document.write( "So we have the equation\r\n" );
document.write( "\r\n" );
document.write( "                  1/30 + 1/45 + 1/90 = 1/x\r\n" );
document.write( "\r\n" );
document.write( "                \r\n" );
document.write( "\r\n" );
document.write( "Now to clear of fractions, we multiply every term through by the \r\n" );
document.write( "LCD of 90x\r\n" );
document.write( "\r\n" );
document.write( "                \r\n" );
document.write( "\r\n" );
document.write( "                 \r\n" );
document.write( "                        \r\n" );
document.write( "                      \r\n" );
document.write( "\r\n" );
document.write( "                                                    \r\n" );
document.write( "\r\n" );
document.write( "So it would take all three 15 minutes.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );